(b) Note that the point \((i)\)  shows that if an operator \(T\)  is defined on \(L^p_w(X)\)  for every \(w\in A_p\) , then \(Tf\)  makes sense for every \(f \in \Phi (X)\) , where \(\Phi \)  satisfies the assumption of Theorem REF . Therefore, no further extension procedure for such operator \(T\)  is needed. Cf. [1]}; see also Remark REF (b) below.

